The Troublesome Probabilistic Powerdomain

Achim Jung, Regina Tix
1998 Electronical Notes in Theoretical Computer Science  
In 12] it is shown that the probabilistic powerdomain of a continuous domain is again continuous. The category of continuous domains, however, is not cartesian closed, and one has to look at subcategories such as RB, the retracts of bi nite domains. 8] o ers a proof that the probabilistic powerdomain construction can be restricted to RB. In this paper, we g i v e a c o u n terexample to Graham's proof and describe our own attempts at proving a closure result for the probabilistic powerdomain
more » ... struction. We have positive results for nite trees and nite reversed trees. These illustrate the di culties we face, rather than being a satisfying answer to the question of whether the probabilistic powerdomain and function spaces can be reconciled. We are more successful with coherent or Lawson-compact domains. These form a category with many pleasing properties but they fall short of supporting function spaces. Along the way, we g i v e a new proof of Jones' Splitting Lemma.
doi:10.1016/s1571-0661(05)80216-6 fatcat:fdmae4p3cneldf6g4h73radoqi